# Activity & The Decay Constant(OCR A Level Physics)

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Katie M

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Physics

## Activity & The Decay Constant

• Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei which are expected to decay per unit time
• This is known as the average decay rate

• As a result, each radioactive element can be assigned a decay constant
• The decay constant λ is defined as:

The probability, per second, that a given nucleus will decay

• When a sample is highly radioactive, this means the number of decays per unit time is very high
• This suggests it has a high level of activity

• Activity, or the number of decays per unit time can be calculated using:

• Where:
• A = activity of the sample (Bq)
• ΔN = number of decayed nuclei
• Δt = time interval (s)
• λ = decay constant (s-1)
• N = number of nuclei remaining in a sample

• The activity of a sample is measured in Becquerels (Bq)
• An activity of 1 Bq is equal to one decay per second, or 1 s-1

• This equation shows:
• The greater the decay constant, the greater the activity of the sample
• The activity depends on the number of undecayed nuclei remaining in the sample
• The minus sign indicates that the number of nuclei remaining decreases with time - however, for calculations it can be omitted

#### Worked example

Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq.

(a)
Determine the number of nuclei in the sample of americium-241.
(b)
Determine the decay constant of americium-241.

Part (a)

Step 1: Write down the known quantities

• Mass = 5.1 μg = 5.1 × 10-6 g
• Molecular mass of americium = 241

Step 2: Write down the equation relating number of nuclei, mass and molecular mass

Step 3: Calculate the number of nuclei

Part (b)

Step 1: Write the equation for activity

Activity, A = λN

Step 2: Rearrange for decay constant λ and calculate the answer

#### Exam Tip

There are lots of new symbols and definitions in this unit. Make sure you are clear on what each symbol means.

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